AXISYMMETRIC VIBRATIONAL BENDING OF THICK-WALLED CYLINDRICAL SHELL OF VISCOELASTIC MATERIAL UNDER ARBITRARY FIXING OF SECTIONS

Abstract

Stable axisymmetric vibrations of a thick-walled circular cylindrical shell made of a visco-elastic material are examined under pressure distributed in cylindrical surfaces which changes in time according to the law of harmonic. A system of four partial differential equations of the second order for defining the constituents of radial and axial displacements is written without any preliminary suppositions about the character of changes in unknown values on thickness. A spline-collocation method is used for decreasing the system dimension under an arbitrary way of fixing of sections. A corresponding boundary problem is numerically solved using a discrete Godunov method of orthogonalization.
As an example the vibrations of shells with the same radius of the surface under various values of length and thickness. A comparison of results according to a strict and classic theory based on Kirchhoff−Love hypotheses is performed. Some peculiarities of changes on the radius of the radial displacement constituents which can not be detected in the frames of any approximated theory, assuming constancy of bending on the shell thickness are noted.

Key words: axisymmetric vibrational bending, thick-walled cylindrical shell, visco-elastic material.